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The density of states of the disordered s-wave superconductor is calculatedperturbatively. The effect of Coulomb interaction on diffusively movingelectrons in the normal state has been known before, but in the superconductingstate both diffuson and the screened Coulomb interaction are modified.Therefore, the correction to the density of states in the superconducting stateexhibits an energy dependence different from that of the normal state. There isa dip structure in the correction part because the interaction has a peak attwice the energy of the superconducting gap. The Coulomb interaction and thesuperconducting fluctuation cannot be treated separately because the densityfluctuation is coupled to the phase fluctuation in the superconducting state.This coupling results in the absence of divergence around the gap edge in thecorrection part, which suggests the validity of this perturbation calculation.

Effect of Coulomb Interaction and Disorder on Density of States in Conventional Superconductors